Course detail
Theory of errors and adjustment 2
FAST-BEA013Acad. year: 2022/2023
Geodetic task, kinds and types of adjustment, indirect observations adjustment and it's quality assessment, conditional observations adjustment and it's quality assessment, combined adjustments, heterogenous observations adjustment, regression analysis, testing of statistical hypotheses and systematic errors, correlation analysis, error ellipses and ellipsoides.
Language of instruction
Czech
Number of ECTS credits
5
Mode of study
Not applicable.
Guarantor
Department
Institute of Geodesy (GED)
Learning outcomes of the course unit
Student gets knowledge of ways of principle of conditions adjustment and solutions the other complicated types of adjustment problems, regression analysis and analysis of correlation.
Prerequisites
Geodetical surveying and computation of measurements on the plane, similar for heights, linear algebra – matrix calculus and processing systems of linear equations, analytical geometry, derivative of functions, Taylors expansion of a function, characteristics of position and variability of random variable, covariance matrix, laws of error propagation, weigth matrix, Least squares method, use of calculator, table processors and matrix oriented programming environment.
Co-requisites
Not applicable.
Planned learning activities and teaching methods
Not applicable.
Assesment methods and criteria linked to learning outcomes
Not applicable.
Course curriculum
1. Purpose and content of the subject, requiements for obtaining the credit and passing the exam, information sources. Geodetic task, conditions of resolvability, kinds and types of adjustment.
2. Procedure of indirect observations adjustment.
3. Indirect observations adjustment - quality assessment.
4. Procedure of conditional observations adjustment.
5. Conditional observations adjustment - quality assessment.
6. Solution of conditional observations adjustment by conversion to indirect observations adjustment, adjustment of given sum, indirect observations adjustment with conditions.
7. Conditional observations adjustment with unknowns, adjustment of heterogenous observations.
8. Regression analysis, approximation by a polynom.
9. Linear regression, regression plane, harmonic analysis.
10. Testing of statistical hypotheses.
11. Testing of systematic errors.
12. Testing of outliers, law of total errors propagation.
13. Analysis of variance, correlation analysis, error ellipses and ellipsoides.
1. Principle of condition Adjustment.
2. Condition, misclosure, and linearization condition equations.
3. Solution of normal equations, correlates, standard deviations.
4. the other types of adjustment, mixed adjustment.
5. Test of observations, simple statistic tests.
6. Test of normal distribution of sample.
7. Analysis of systematic errors in observations.
8. Analysis of parameters.
9. Linear regression - line fitting.
10. Regression analysis - regression curves.
11. Harmonic functions.
12. Analyssis of corelation, physical and mathematical corelation.
13. Helmert curve, error ellipsis, error ellipsoides. Laws of propagation corelation observations.
2. Procedure of indirect observations adjustment.
3. Indirect observations adjustment - quality assessment.
4. Procedure of conditional observations adjustment.
5. Conditional observations adjustment - quality assessment.
6. Solution of conditional observations adjustment by conversion to indirect observations adjustment, adjustment of given sum, indirect observations adjustment with conditions.
7. Conditional observations adjustment with unknowns, adjustment of heterogenous observations.
8. Regression analysis, approximation by a polynom.
9. Linear regression, regression plane, harmonic analysis.
10. Testing of statistical hypotheses.
11. Testing of systematic errors.
12. Testing of outliers, law of total errors propagation.
13. Analysis of variance, correlation analysis, error ellipses and ellipsoides.
1. Principle of condition Adjustment.
2. Condition, misclosure, and linearization condition equations.
3. Solution of normal equations, correlates, standard deviations.
4. the other types of adjustment, mixed adjustment.
5. Test of observations, simple statistic tests.
6. Test of normal distribution of sample.
7. Analysis of systematic errors in observations.
8. Analysis of parameters.
9. Linear regression - line fitting.
10. Regression analysis - regression curves.
11. Harmonic functions.
12. Analyssis of corelation, physical and mathematical corelation.
13. Helmert curve, error ellipsis, error ellipsoides. Laws of propagation corelation observations.
Work placements
Not applicable.
Aims
After completing the course, the students should be able touse the complicated types of adjustment and fitting.
Specification of controlled education, way of implementation and compensation for absences
Extent and forms are specified by guarantor’s regulation updated for every academic year.
Recommended optional programme components
Not applicable.
Prerequisites and corequisites
Not applicable.
Basic literature
Not applicable.
Recommended reading
Not applicable.
Classification of course in study plans
- Programme BPC-GK Bachelor's 2 year of study, winter semester, compulsory
Type of course unit
Lecture
26 hod., optionally
Teacher / Lecturer
Syllabus
1. Purpose and content of the subject, requiements for obtaining the credit and passing the exam, information sources. Geodetic task, conditions of resolvability, kinds and types of adjustment.
2. Procedure of indirect observations adjustment.
3. Indirect observations adjustment - quality assessment.
4. Procedure of conditional observations adjustment.
5. Conditional observations adjustment - quality assessment.
6. Solution of conditional observations adjustment by conversion to indirect observations adjustment, adjustment of given sum, indirect observations adjustment with conditions.
7. Conditional observations adjustment with unknowns, adjustment of heterogenous observations.
8. Regression analysis, approximation by a polynom.
9. Linear regression, regression plane, harmonic analysis.
10. Testing of statistical hypotheses.
11. Testing of systematic errors.
12. Testing of outliers, law of total errors propagation.
13. Analysis of variance, correlation analysis, error ellipses and ellipsoides.
1. Principle of condition Adjustment.
2. Condition, misclosure, and linearization condition equations.
3. Solution of normal equations, correlates, standard deviations.
4. the other types of adjustment, mixed adjustment.
5. Test of observations, simple statistic tests.
6. Test of normal distribution of sample.
7. Analysis of systematic errors in observations.
8. Analysis of parameters.
9. Linear regression - line fitting.
10. Regression analysis - regression curves.
11. Harmonic functions.
12. Analyssis of corelation, physical and mathematical corelation.
13. Helmert curve, error ellipsis, error ellipsoides. Laws of propagation corelation observations.
Exercise
26 hod., compulsory
Teacher / Lecturer
Syllabus
1. Introduction, envelope, basics of numerics.
2. Test, examples of indirect observations adjustment up to residual equations.
3. Test, exercise Indirect observations adjustment - classical notation.
4. Exercise Indirect observations adjustment - matrix notation.
5. Test, examples of conditional observations adjustment up to linearized condition equations.
6. Exercise Conditional observations adjustment - classical notation.
7. Test, exercise Conditional observations adjustment - matrix notation.
8. Exercise Conditional observations adjustment - heterogenous observations.
9. Test, consultation of the exercise Conditional observations adjustment - heterogenous observations, spare.
10. Exercise Regression analysis.
11. Test, exercise Testing of statistical hypotheses and systematic errors.
12. Consultation and correction of all the exercises, spare.
13. Checking fulfilment requirements and granting credits.